Problem: Solve for $x$ and $y$ using elimination. ${2x-3y = -15}$ ${-2x-5y = -57}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. $-8y = -72$ $\dfrac{-8y}{{-8}} = \dfrac{-72}{{-8}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {2x-3y = -15}\thinspace$ to find $x$ ${2x - 3}{(9)}{= -15}$ $2x-27 = -15$ $2x-27{+27} = -15{+27}$ $2x = 12$ $\dfrac{2x}{{2}} = \dfrac{12}{{2}}$ ${x = 6}$ You can also plug ${y = 9}$ into $\thinspace {-2x-5y = -57}\thinspace$ and get the same answer for $x$ : ${-2x - 5}{(9)}{= -57}$ ${x = 6}$